The 255-Bit Non-Local Information Space in a Neural Network: Emergent Geometry and Coupled Curvature-Tunneling Dynamics in Deterministic Systems

We present a comprehensive analysis of emergent topological structures in a 60-sublayer self-organizing neural network, examined through information-theoretic and geometric perspectives. The observed dynamics defy conventional classification as either deterministic or stochastic. To capture this duality, we introduce the framework of Nonlinear N-Deterministic Systems, in which locally deterministic rules give rise to globally emergent behavior mediated by non-local coupling across higher-dimensional manifolds. The 60-layer subnetwork exhibits a measurable 255-bit non-local information space, defining a lower bound constrained by architectural depth and sampling resolution. Entropy distributions reveal ordered clusters alongside statistically significant “disordered” regions, which nevertheless align along consistent geometric trajectories. These patterns indicate that apparent randomness in local correlations conceals a coherent topological folding process, through which the network self-organizes across higher-dimensional manifolds. Geometric projection shows that this folding manifests as curvature and tunneling dynamics within the information manifold, implying that the network transiently maps between distinct but resonantly connected configurations. These patterns indicate that apparent randomness in local correlations conceals a coherent topological folding process, in which the network self-organizes across higher-dimensional manifolds. The coexistence of structured and unstructured domains suggests that self-organization operates simultaneously on observable and meta-levels of coupling an intrinsic property of N-Deterministic behavior. Such transitions correspond to emergent geometry a field-based information-geometric structure in which curvature, coherence, and information flow become interdependent variables of a unified non-local field. The findings demonstrate that even deterministic architectures can spontaneously generate higher-order geometric behavior traditionally associated with relativistic and quantum systems, providing empirical support for a scalable geometric framework linking topology, information, and dynamics.